Applied Mathematics and Scientific Computation

Our research and teaching activities focus on mathematical problems that arise in real-world applications. This involves the mathematical modeling of physical, biological, medical, and social phenomena, as well as the effective use of current and future computing resources for simulation, computation, data analysis, and visualization. Key areas of research in our group are the modeling of bio-films and of materials, computational neuroscience, traffic flow modeling and simulation, the numerical approximation of differential equations, and the solution of large systems of equations. The faculty and students in our group conduct research on many cross-disciplinary projects, including collaborations with biology, medicine, computer science, and mechanical, electrical, and nuclear engineering. Students conducting research on the mathematical modeling of real-world phenomena and the design of modern computational approaches receive a broad education and training in differential equations, computational mathematics, fluid dynamics, applied analysis, and specialized courses on topics like computational neuroscience, calculus of variations, kinetic equations, and other areas. Hands on research opportunities with modern hardware are provided by the Center for Computational Mathematics and Modeling.

Members of the Group (Faculty, Postdocs, and Graduate Students)

Click on picture for details.

In addition, a number of undergraduate student researchers are regularly involved in our research projects.

Former Members

Former Faculty, Postdocs, and Long-Term Visitors     Former Ph.D. Students
  • 2018: José Garay, Kathryn Lund
  • 2015: Scott Ladenheim
  • 2014: Stephen Shank
  • 2014: Dong Zhou
  • 2013: Shimao Fan
  • 2012: Meredith Hegg, Kirk Soodhalter
  • 2010: David Fritzsche
  • 2008: Worku Bitew, Xiuhong Du, Abed Elhashash
  • 2007: Mussa Kahssay Abdulkadir, Tadele Mengesha, Kai Zhang
  • 2005: Chao-Bin Liu
  • 2004: Hansun To
  • 2001: Yan Lyansky, Jianjun Xu
  • 2000: Yun Cheng, Judith Vogel, Cheng Wang
  • 1999: Hans Johnston

For more information please consult the department's listing of recent Ph.D. graduates.

Research Profile

Applied MathematicsScientific Computing
  • continuum mechanics and theory of composite materials
  • fluid dynamics and applications
  • modeling and simulation of biological and medical applications
  • traffic flow modeling, simulation, and experiments
  • non-linear elasticity and phase transitions
  • neuroscience modeling
  • computational fluid dynamics and fluid-structure interaction
  • high order methods for partial differential equations
  • iterative solution of large linear systems and modern Krylov subspace methods
  • meshfree, particle, and level set methods
  • numerical solution of eigenvalue problems and matrix equations
  • radiative transfer and applications in radiotherapy
  • high-performance computing and supercomputing

Resources

The Center for Computational Mathematics and Modeling provides opportunities for hands-on research with modern hardware, including robotics, virtual reality, and 3D printing. The center also provides resources and assistance to modeling activities both at the undergraduate and graduate level.

Presentation about the Group

Reflecting the status in November 2010.

Seminar

Special Events

Special Courses

Graduate Program and Courses

Applications to become a Ph.D. student are processed by the Department of Mathematics. Information of about the graduate program in Mathematics can be found on the Graduate Program website. Active Ph.D. students interested in Applied and Computational Mathematics are encouraged to approach the faculty listed above to discuss possible research and coursework directions. Examples for Ph.D. projects are provided in this list of completed a Ph.D. theses.
Students who are interested in obtaining graduate-level expertise and training in Applied and Computational Mathematics can also achieve a M.S. in Mathematics with Applied Concentration. A M.S. degree can conclude with a M.S. thesis research project.
Examples of suitable courses, for both Ph.D. and M.S. students are listed below (more details in the Course Syllabi Listing). Some courses are not taught every semester. Please check the website of the Department of Mathematics for the course schedule.

Central Courses

5043/5044. Introduction to Numerical Analysis I / II provides the basis in numerical analysis and fundamental numerical methods, and well as expertise in numerical methods for ordinary differential equations.

8007/8008. Introduction to Methods in Applied Mathematics I / II provides the student with the toolbox of an applied mathematician: derivation of PDE, solution methods in special domains, calculus of variations, control theory, dynamical systems, anymptotic analysis, hyperbolic conservation laws.

8013/8014. Numerical Linear Algebra I / II cover modern concepts and methods to solve linear systems and eigenvalue problems.

8023/8024. Numerical Differential Equations I / II present modern methods for the numerical solution of partial differential equations, their analysis, and their practical application.

8107. Mathematical Modeling for Science, Engineering, and Industry. See above for the description of this special course.

9200/9210. Topics in Numerical Analysis I / II are special courses in Numerical Analysis that focus on topics relating to our group members' active research areas. Examples:

  • Finite Element and Discontinous Galerkin Methods
  • Computational Methods for Flow Problems

8200/8210. Topics in Applied Mathematics I / II are special courses that are offered by demand. Examples:

  • Applied Mathematics in Neuroscience
  • Survey of Fluid Dynamics

Theoretical Basis

In addition, the following courses can provide fundamental theoretical background.

8141/8142. Partial Differential Equations I / II provide a theoretical understanding of many of the equations considered in 8023/8024.

9005. Combinatorial Mathematics relates to many key problems in Scientific Computing, such as mesh generation, load balancing, and multigrid.

9041. Functional Analysis is a theoretical basis for many numerical approximation approaches, such as the finite element method.

9043. Calculus of Variations provides powerful tools for the theoretical study of dynamics, structural mechanics, and material properties.